Xin Zhou

The volume spectrum is an analogue of the Laplace spectrum, defined through the area functional together with homological or cohomological relations in the space of hypercycles. In this talk, I will introduce several versions of the volume spectrum...

I will present a joint work with Martin Li. Minimal surfaces with free boundary are natural critical points of the area functional in compact smooth manifolds with boundary. In this talk, I will describe a general existence theory for minimal...

I will present a recent proof of the Multiplicity One Conjecture in Min-max theory. This conjecture was raised by Marques and Neves. It says that in a closed manifold of dimension between 3 and 7 with a bumpy metric, the min-max minimal hypersurfaces...